element tally of pearl ash

pearl ash | elemental composition

Find the elemental composition for pearl ash in terms of the atom and mass percents: atom percent = N_i/N_atoms × 100% mass percent = (N_im_i)/m × 100% Plan: • Write the chemical formula and gather atomic masses from the periodic table. • Determine values for N_i, m_i, N_atoms and m using these items. • Finally, compute the percents and check the results. Write the chemical formula: K_2CO_3 Use the chemical formula to count the number of atoms, N_i, for each element and find the total number of atoms, N_atoms, per molecule: | number of atoms C (carbon) | 1 K (potassium) | 2 O (oxygen) | 3 N_atoms = 1 + 2 + 3 = 6 Divide each N_i by N_atoms to calculate atom fractions. Then use the property that atom fractions must sum to one to check the work: | number of atoms | atom fraction C (carbon) | 1 | 1/6 K (potassium) | 2 | 2/6 O (oxygen) | 3 | 3/6 Check: 1/6 + 2/6 + 3/6 = 1 Compute atom percents using the atom fractions: | number of atoms | atom percent C (carbon) | 1 | 1/6 × 100% = 16.7% K (potassium) | 2 | 2/6 × 100% = 33.3% O (oxygen) | 3 | 3/6 × 100% = 50.0% Look up the atomic mass, m_i, in unified atomic mass units, u, for each element in the periodic table: | number of atoms | atom percent | atomic mass/u C (carbon) | 1 | 16.7% | 12.011 K (potassium) | 2 | 33.3% | 39.0983 O (oxygen) | 3 | 50.0% | 15.999 Multiply N_i by m_i to compute the mass for each element. Then sum those values to compute the molecular mass, m: | number of atoms | atom percent | atomic mass/u | mass/u C (carbon) | 1 | 16.7% | 12.011 | 1 × 12.011 = 12.011 K (potassium) | 2 | 33.3% | 39.0983 | 2 × 39.0983 = 78.1966 O (oxygen) | 3 | 50.0% | 15.999 | 3 × 15.999 = 47.997 m = 12.011 u + 78.1966 u + 47.997 u = 138.2046 u Divide the mass for each element by m to calculate mass fractions. Then use the property that mass fractions must sum to one to check the work: | number of atoms | atom percent | mass fraction C (carbon) | 1 | 16.7% | 12.011/138.2046 K (potassium) | 2 | 33.3% | 78.1966/138.2046 O (oxygen) | 3 | 50.0% | 47.997/138.2046 Check: 12.011/138.2046 + 78.1966/138.2046 + 47.997/138.2046 = 1 Compute mass percents using the mass fractions: Answer: | | | number of atoms | atom percent | mass percent C (carbon) | 1 | 16.7% | 12.011/138.2046 × 100% = 8.691% K (potassium) | 2 | 33.3% | 78.1966/138.2046 × 100% = 56.58% O (oxygen) | 3 | 50.0% | 47.997/138.2046 × 100% = 34.73%

Mass fraction pie chart